Asymmetry Driven Phase Transformations

Abstract

Motivated by the properties of one-dimensional lattice systems with asymmetric on-site potential, one can formulate a hypothesis of an asymmetry driven phase transformation. Characteristic feature of one-dimensional systems exhibiting asymmetry driven phase transformation is a sequence of the two phase conversions. In particular class of such systems with a triple-well potential, phase conversions of one-dimensional systems would evolve into a sequence of two phase transitions in three-dimensional models. We propose here a model of three-dimensional system exhibiting a sequence of two first order asymmetry driven phase transitions.PACS numbers: 05.70.−a, 64.60.−i, 63.70.+h MotivationIn the thermodynamic regime, one-dimensional (1D) lattice systems with degenerated vacuum, reveal the coexistence of localized and extended excitations, kinks and phonons, respectively, that is accompanied by characteristic hump developed in a specific heat [1,2]. Three--dimensional (3D) version of such a system exhibits phase transition of second order. In fact, it is one of the simplest manifestations of spontaneously broken (discrete) symmetry.It has been recently observed [3,4] that one--dimensional, multistable systems, with non-degenerated vacuum would exhibit interesting behavior. Specific heat of systems with local asymmetric, double-well or triple--well potential, may reveal quite rich, two-peak structure, possibly corresponding to two phase conversions. One can ask whether such a property of one-dimensional systems, would indicate a sequence of the phase transitions in corresponding three-dimensional systems.The aim of this paper is to give a comprehensive analysis of unconventional behaviour of specific heat of a class of one-dimensional lattice systems with triple-well potential. It is argued that large, shape-type asymmetry of these systems is manifested by "energy level crossing", associated with two-peak structure of specific heat. In this case it reflects a sequence of two phase conversions. These phase conversions would turn into phase transitions in three-dimensional version of the model. We propose here a model of a three-dimensional lattice system exhibiting a sequence of two phase transitions -they may be referred to as asymmetry driven phase transitions. The